It might correct the problem. Other possible problems could be corroded battery cables, dirty grounds, weak battery, etc. First step is to do a vehicle charging system check, and a battery load test. The PCM's internal voltage regulator is not the usual cause of a charging system problem.

I've seen the test machines at the auto parts stores for off the vehicle alternators and starters pass defective units and fail good units.

No, you'll need the same year that you have, in this case a 1993. As ratmonkey already explained, if you're getting one from the auto salvage you'll need to find one with the same part number as is on the label on yours. You need one with the same engine as you have, and whether or not your ZJ and the donor ZJ have security is very important. You can't mix those.